Simplify (4x^4)^3(2xy^3)^2

${(4 x^{4})}^{3} {(2 x y^{3})}^{2}$

Apply the product rule to $4 x^{4}$ .

$4^{3} {(x^{4})}^{3} {(2 x y^{3})}^{2}$

Raise $4$ to the power of $3$ .

$64 {(x^{4})}^{3} {(2 x y^{3})}^{2}$

Multiply the exponents in ${(x^{4})}^{3}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$64 x^{4 \cdot 3} {(2 x y^{3})}^{2}$

Multiply $4$ by $3$ .

$64 x^{12} {(2 x y^{3})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Apply the product rule to $2 x y^{3}$ .

$64 x^{12} ({(2 x)}^{2} {(y^{3})}^{2})$

Apply the product rule to $2 x$ .

$64 x^{12} (2^{2} x^{2} {(y^{3})}^{2})$

Multiply $x^{12}$ by $x^{2}$ by adding the exponents.

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Move $x^{2}$ .

$64 (x^{2} x^{12}) (2^{2} {(y^{3})}^{2})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$64 x^{2 + 12} (2^{2} {(y^{3})}^{2})$

Add $2$ and $12$ .

$64 x^{14} (2^{2} {(y^{3})}^{2})$

Rewrite using the commutative property of multiplication.

$64 \cdot 2^{2} (x^{14} {(y^{3})}^{2})$

Raise $2$ to the power of $2$ .

$64 \cdot 4 (x^{14} {(y^{3})}^{2})$

Multiply $64$ by $4$ .

$256 (x^{14} {(y^{3})}^{2})$

Multiply the exponents in ${(y^{3})}^{2}$ .

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Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$256 (x^{14} y^{3 \cdot 2})$

Multiply $3$ by $2$ .

$256 (x^{14} y^{6})$

$256 x^{14} y^{6}$

Simplify (4x^4)^3(2xy^3)^2

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